It appears that you have chin and jawline asymmetry due to a difference in the height of the bone. An intraoral approach to shaving down the longer side of the chin and front operation of the jawline behind it would be the recommended surgery. Whether this will improve the lip pulling is unknown.
Correcting an asymmetric jawline
Hi Anna -From the photo and your description, it might be possible to something rather minor to fix your issue. The "dent" you see on the sides of the chin looks a little deeper on the left side. The muscle that pulls the lip down start down around there. If you go to surgeon near you, one who is very deft with tissues around the mouth, he may be able to inject some filler deep along the bone to make thing more symmetical with the right side and in the process decrease the "mechanical advantage" of the muscle - making your lip movements more symmetrical. I suggest trying a hyaluronic filler first (Resylane Lyft?), so that you can melt it if it doesn't work.I hope this helps!Rob